Accumulating transformations for hierarchical linear regression HMM adaptation

ABSTRACT

A new method, which builds the models at m-th step directly from models at the initial step, is provided to minimize the storage and calculation. The method therefore merges the M×N transformations into a single transformation. The merge guarantees the exactness of the transformations and make it possible for recognizers on mobile devices to have adaptation capability.

FIELD OF INVENTION

[0001] This invention relates to speech recognition and more particularly to adaptive speech recognition with hierarchical linear HMM adaptation.

BACKGROUND OF INVENTION

[0002] Hierarchical Linear Regression (HLR) (e.g. MLLR [See C. J. Leggetter and P. C. Woodland, Maximum likelihood Linear regression for speaker adaptation of continuous density HMMs, Computer, Speech and Language, 9(2):71-185,1995] is now a common technique to transform Hidden Markov Models (HMM) models for use in an acoustic environment different from the one the models are initial trained. The environments refer to speaker accent, speaker vocal tract, background noise, recording device, transmission channel, etc. HLR improves word error rate (WER) substantially by reducing the mismatch between training and testing environments [See C. J. Leggetter cited above].

[0003] Hierarchical Linear Regression (HLR) (e.g. MLLR or Maximum Likelihood Linear Regression) is an interactive process that transforms an initial Hidden Markov Model (HMM) models step-by-step into a target model. Typically, the iteration requires M alignments of transformed HMM against speech data and each alignment results are used to produce new transformations through N EM re-estimations. Thus M×N steps are required.

[0004] Current methods build the models at m-th step from models at m−1-th step. Each step produces a set of transformations that is used by the step next to it. To reproduce the target models, the M×N transformations have to be stored and later applied to the initial models.

[0005] Current methods build the models at m-th step from models at m−1-th step. Each step produces a set of transformations EM (Expectation Maximization) that is used by the step next to it, as illustrated in FIG. 1. At he recognition time, to get the target models, two alternatives can be considered. The first is to store the model set obtained at the M×N transformations. As typical continuous speech recognizers may use tens of thousands of mean vectors, storing the additional parameters of that size is unaffordable for situations as in speech recognition on mobile devices. The second is to apply successively the M×N transformations to the initial model set, as illustrated by FIG. 2. This requires storing the M×N transformations. Typically the storage requirement is substantially lower. However, it is still prohibitive for typical embedded systems such as a DSP based one. Notice that, as represented by the size of the boxes in FIG. 2, the number of transformations in each transformation step may be different.

SUMMARY OF INVENTION

[0006] A new method, which builds the models at m-th step directly from models at the initial step, is provided to minimize the storage and calculation. The method therefore merges the M×N transformations into a single transformation. The merge guarantees the exactness of the transformations and make it possible for recognizers on mobile devices to have adaptation capability. The goal of the method to be described is to provide a single set of transformations which combines all M×N set of transformations, so that a target model at any iteration can be calculated directly from initial model and the single set of transformations. FIG. 3 illustrates the goal.

[0007] The combination guarantees the exactness of the total transformations, i.e. the resulting models obtained by the single set of transformations are the same as the target models obtained by successive applications of transformations. This results make it possible for recognizers on mobile devices to have adaptation capability.

DESCRIPTION OF DRAWINGS

[0008]FIG. 1 illustrates types of iterations;

[0009]FIG. 2 illustrates Target models are obtained by successive application of several set of transformations T₁, T₂.

[0010]FIG. 3 illustrates Target models are obtained by a single application of one set of transformations T.

[0011]FIG. 4 illustrates part of a regression tree.

[0012]FIG. 5 illustrates the operation according to one embodiment of the present invention.

[0013]FIG. 6 illustrates the system according to one embodiment of the present invention.

DESCRIPTION OF PREFERRED EMBODIMENT

[0014] In accordance with the present invention the method builds the models at the m-th step directly from models at the initial step by successive applications of transformations as illustrated in FIGS. 3 and 5. The algorithms for providing this are derived herein in the following.

[0015] Let Ξ={ξ₁, ξ₂, . . . ξN} be the set of nodes of the regression tree. Leaf nodes Ω⊂Ξ of the tree correspond to a class. A class can be either a HMM, a cluster of distributions, a state PDF, etc., depending on the adaptation scheme. A leaf node a αεΩ is assigned the number m(αi) of acoustic vectors associated to the node at iteration. i.

[0016] For illustration, FIG. 4 shows part of a tree with leaves corresponding to phone HMM.

[0017] We introduce the function

φ:Ξ

Ξ

[0018] such that ξ_(j)=Φ(ξ_(i))i≠j is the root of the node ξ_(i). Similarly, we introduce the function

φ:Ξ×[0,1]

Ξ

[0019] such that ξ=Φ(Φ(ξ,i)), i.e. l(ξ,i) is the i-th descendent of the node ξ.

[0020] At each iteration of parameter estimation, to each node is associated a number ρ(ξ,i) recording the total number of input vectors under the node. ${\rho \left( {\xi,i} \right)} = \left\{ \begin{matrix} {m\left( {\xi,i} \right)} & {{if}\quad \xi \quad \varepsilon \quad \Omega} \\ {\sum_{i}{\rho \left( {\xi,i} \right)}} & {otherwise} \end{matrix} \right.$

[0021] A node is called reliable if

ρ(ξ,i)>P

[0022] where P is a constant, fixed for each alignment. The function

ψ:Ξ×N

[False,True]

[0023] such that ψ(ξ,i) indicates if a node is reliable at the i-th iteration. Note that at each iteration, as the alignment between leaf nodes and speech signals may change, ψ is a function of i. Only reliable nodes are assigned a transformation T_(ξ) ^(i). Each leaf node, e.g. each HMM, has its transformation located on the first reliable node given by recursively tracing back to the roots.

[0024] Another function we introduce is

χ:Ξ×N

Ξ

[0025] such that ζ=χ(ξ,i) is the first root node of ξ that satisfies ψ (ζ,i)=True.

[0026] We use general form for linear regression transformation, which applies a linear transformation T to the mean vector of Gaussian distributions:

{circumflex over (μ)}=T(μ)=Aμ+B

[0027] where A is a D×D matrix, and: a D-dimensional column vector, and B a D-dimensional column vector. We assume that at any step, the current model is always obtained by transforming the initial model. I.e. We always map the original models:

∀n∀ξ,{circumflex over (μ)}_(n) =T _(n,ξ)(μ₀)=A _(n,ξ)μ₀ +B _(n,ξ)

[0028] Referring to FIG. 1, we distinguish two types of parameter estimation iterations: between EM and between alignment iterations. Correspondingly, in the next two sections we will study two types of transformation combinations:

[0029] Transformation accumulation between EM estimations.

[0030] Transformation accumulation between alignment iterations.

[0031] Transformation accumulation between EM estimations

[0032] Given

[0033] The set of transformations that maps the initial models through n−1 EM re-estimations (global at n−1).

[0034] The set of transformations that maps the models at n=1-th iteration to the models at the iteration n (local at n).

[0035] We want to find the set of accumulated transformations, global at n, which combines the global at n−1 and local at n (local at n).

[0036] As between two EM the alignment is fixed, the reliable node information is unchanged. Therefore the association between nodes and transformations is fixed from at the two EM iterations.

[0037] At any given alignment, for each ξεΞ and ψ(ξ,i), let A_(n−1,ξ) and B_(n−1,ξ) be the global transformation derived at EM iteration n−1, and A_(n,ξ) and B_(n,ξ) be the local transformation derived at EM iteration n. Then a single transformation Â_(n,ξ) and {circumflex over (B)}_(n,ξ) is combined from the two transformations.

[0038] Proposition 1 ∀ξεΞΛψ(ξ,i) where Λ is global,

(Â _(n−1,ξ) , {circumflex over (B)} _(n−1,ξ))⊕(Â _(n,ξ) ,{circumflex over (B)} _(n,ξ))Δ(Â _(n,ξ) ,{circumflex over (B)} _(n,ξ))

[0039] With

{Â _(n,ε) =A _(n1ξ) Â _(n−1,ξ) Â _(0,ξ) =I

{{circumflex over (B)} _(n,ξ) =A _(n1ξ) {circumflex over (B)} _(n−1,ξ) +B _(n1ξ) {circumflex over (B)} _(0,ξ) =0

[0040] PROOF:

[0041] The case n=1 corresponds to a single transformation and correctness of Eq-5 is obvious. For n >1, using Eq-3:

μ_(n) =A _(n,ξ)μ_(n−1,ξ) +B _(n,ξ)

=A _(n,ξ)(Â _(n−1,ξ)μ₀ +{circumflex over (B)} _(n−1,ξ))+B _(n,ξ)

=(A _(n,ξ) Â _(n,ξ) Â _(n−1,ξ))μ₀+(A _(n,ξ) {circumflex over (B)} _(n−1,ξ) +B _(n,ξ))

=Â _(n,ξ)μ₀ +B _(n,ξ)

[0042] Transformation accumulation between alignment iterations

[0043] Given

[0044] The set of transformations that maps the initial models through i−1 alignments (global at i−1).

[0045] The set of transformations that maps the models at i−1 -th alignment to the models at the alignment i (local at i).

[0046] We want to find the set of accumulated transformations, global at i, which combines the global at i−1 and locate at i transformations.

[0047] Different from the accumulation between two EM iterations, the alignment here may be changed, which results in a change in the reliable node information. Therefore the association between nodes and transformations cannot be assumed fixed from i−1 to ilth alignment. For instance, the number of transformations at i is different from that at i−1, for two reasons:

[0048] The value of P in Eq-2 may be different. Typically, P is decreased to increase the number of transformations as i increases.

[0049] Even if P is kept constant a cross alignment, as the acoustic model parameters are changed at each alignment, ρ(ξ,i)may change as function of i, so will ψ(ξ,i).

[0050] The combined set of transformations is specified by Eq-10.

[0051] Proposition 2 ∀ξεΞ: $T_{\xi}^{i} = \left\{ \begin{matrix} {T_{\xi}^{i - 1} \oplus T_{\xi}^{i}} & {{if}\quad {\psi \left( {\xi,{i - 1}} \right)}{{\Lambda\psi}\left( {\xi,i} \right)}} \\ {T_{\xi}^{i - 1} \oplus T_{\chi {({\xi,i})}}^{i}} & {{if}\quad {\psi \left( {\xi,{i - 1}} \right)}\Lambda {{\psi \left( {\xi,i} \right)}}} \\ {T_{\chi {({\xi,{i - 1}})}}^{i - 1} \oplus T_{\xi}^{i}} & {{if}\quad {{{\psi \left( {\xi,{i - 1}} \right)}{{\Lambda\psi}\left( {\xi,i} \right)}}}} \\ {None} & {Otherwise} \end{matrix} \right.$

[0052] PROOF:

[0053] ∀ξεΞ, only one of four situations can happen:

[0054] 1. It is a reliable node at both iterations i−1 and i. The parameters of the models under this node are therefore transformed by T^(i−1) _(ξ) and then by T_(ξ) ^(i).

[0055] 2. It is a reliable node at iteration i−1 but not at iteration i. The transformation at i is therefore the one at the node χ(ξ,i) . The parameters of the models under node ξ are therefore transformed by T^(i−1) _(ξ) and then by T_(xξ) ^(i)(ξ, i).

[0056] 3. It is a reliable node at iteration i but not at iteration i−1. The transformation at i−1 is therefore the one at the node χ(ξ,i−1). The parameters of the models under node ξ are therefore transformed by T^(i−1) _(x)(ξ,i−1) and then by T^(i−1) _(ξ).

[0057] 4. It is not a reliable node at both iterations. The node has therefore no transformation.

[0058] In the fourth case, no transformation will be generated.

[0059] Referring to FIG. 6, there is illustrated a system according to one embodiment of the present invention wherein the input speech is compared to models at recognizer 60 wherein the models 61 are HMM models that have had HLR HMM adaptation or training using only a single set of transformation parameters wherein for transformation accumulations between EM estimations equation 4 is used and for transformation accumulation between alignment iterations is according to equation 10. 

1. A method of hierarchical linear regression adaptation of HMM models comprising the steps of: providing HMM models for adaptation to a new acoustic environment and obtaining adapted new models directly from the initial HMM models using a single set of transformations.
 2. The method of claim 1 wherein said obtaining step includes performing transformation accumulation between EM estimations and transformation accumulation between alignment iterations.
 3. A recognizer comprising: a recognizer including adapted HMM models obtained directly from initial HMM models using a single set of transforms.
 4. The recognizer of claim 3 wherein said HMM models are obtained by performing transformation accumulation between EM estimations and transformation accumulation between alignment iterations. 